Answer:
Alan has $23
Leila has $33
Miguel has $46
Explanation:
Let the variables L, A, and M represent the amounts Leila, Alan, and Miguel have.
Step 1: Create an expression to represent Miguel's amount:
Since Miguel has 2 times Alan's amount, we can represent this with the following expression:
M = 2A
Step 2: Create an expression to represent Leila's amount:
Since Leila has $10 more than Alan, we can represent with the following expression:
L = A + 10
Step 3: Set the sum of the expressions and A equal to $102:
We know that L + A + M = 102. Thus, we can plug in 2A for M and A + 10 for L to find A, Alan's amount:
2A + A + A + 10 = 102
4A + 10 = 102
4A = 92
A = 23
Thus, Alan has $23.
Step 4: Find Miguel's amount by plugging in 23 for A in M = 2A:
M = 2(23)
M = 46
Thus, Miguel has $46.
Step 5: Find Leila's amount by plugging in 23 for A in L + A + 10:
L = 23 + 10
L = 33
Thus, Leila has $33.
Step 6: Check that the sum of Leila, Alan, and Miguel's amounts is 102:
We can check that our answers are correct by making sure that the sum of Leila, Alan, and Miguel's amounts (33, 23, and 46 respectively) equals 102:
33 + 23 + 42 = 102
56 + 46 = 102
102 = 102
Thus, our answers are correct.